Space Analyticity for the Navier-Stokes and Related Equations with Initial Data inLp

Abstract

We introduce a method of estimating the space analyticity radius of solutions for the Navier-Stokes and related equations in terms ofLpandL∞norms of the initial data. The method enables us to express the space analyticity radius for 3D Navier-Stokes equations in terms of the Reynolds number of the flow. Also, for the Kuramoto-Sivashinsky equation, we give a partial answer to a conjecture that the radius of space analyticity on the attractor is independent of the spatial period. © 1998 Academic Press.